College Algebra 3

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Factoring
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The process of writing a number or exponent as a product.
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Factorization
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Any combination of factors multiplied together resulting in the product
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Factors
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Any set of the numbers or expressions that form a product
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Prime factorization
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The unique factorization of a natural number written as a product of primes
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Greatest common factor GCF
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Product of all the common prime factors
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Relatively prime
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Expressions that share no common factors other then one
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GCF of monomials
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Product of the GCF of the coefficient and all common variables
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Factoring a polynomial
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The process of rewriting a polynomial as a product of polynomial factors.
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Factoring out the GCF
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The process of rewriting a polynomial as a product using the GCF of all of its terms.
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GCF of a polynomial
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The greatest common factor of all the terms of the polynomial.
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Prime polynomial
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A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself.
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Factor by grouping
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A technique for factoring polynomials with four terms
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Root
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A solution to a quadratic equation in standard form
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Double root
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A root that is repeated twice
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Area of rectangle
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A = lw, where l represents the length and w represents the width.
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Area of square
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A = s2, where s represents the length of each side.
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Area of triangle
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A=1/2 bh, where b represents the length of the base and h represents the height.
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Area of circle
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A = πr2, where r represents the radius and the constant π ≈ 3.14.
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Exponential form
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An equivalent expression written using a rational exponent.
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Product rule for exponents
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xm ⋅ xn = xm+n; the product of two expressions with the same base can be simplified by adding the exponents
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Quotient rule for exponents
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The quotient of two expressions with the same base can be simplified by subtracting the exponents
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Power rule for exponents
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(xm)n = xmn; a power raised to a power can be simplified by multiplying the exponents.
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Power rule for a product
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(xy)n = xnyn; if a product is raised to a power, then apply that power to each factor in the product.
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FOIL
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When multiplying binomials we apply the distributive property multiple times in such a way as to multiply the first terms, outer terms, inner terms, and last terms.
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Check by evaluating
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We can be fairly certain that we have multiplied the polynomials correctly if we check that a few values evaluate to the same results in the original expression and in the answer.
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Square Root
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The number that, when multiplied by itself, yields the original number.
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Principle Square Root
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The positive square root of a real number, denoted with the symbol √.
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Radicand
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The expression a within a radical sign, an.
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Cube Root
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The number that, when used as a factor with itself three times, yields the original number; it is denoted with the symbol 3.
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Index
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The positive integer n in the notation n that is used to indicate an nth root.
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N th Root
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The number that, when raised to the nth power, yields the original number.
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Radical
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Used when referring to an expression of the form an .
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Principle n th Root
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The positive nth root when n is even.
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Product Rules for Radicals
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a⋅bn=an⋅bn, where a and b represent positive real numbers.
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Quotinct Rules for Radicals
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a b n= an bn , where a and b represent positive real numbers.
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Simplified Radicals
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A radical where the radicand does not consist of any factor that can be written as a perfect power of the index.
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Radical Expression
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An algebraic expression that contains radicals.
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Square Root Function
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The function f(x)=(square root)x
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Cube root function
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The function f(x)=x3.
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Like Radicals
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Radicals that share the same index and radicand.
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Similar Radicals
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Term used when referring to like radicals.
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Conjugates
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The factors (a + b) and (a − b) are conjugates.
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Rationalizing the Denominator
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The process of determining an equivalent radical expression with a rational denominator.
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Rational Exponents
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The fractional exponent m/nthat indicates a radical with index n and exponent m: am/n=amn.
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Exponential Form
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An equivalent expression written using a rational exponent.
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Radical Equation
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Any equation that contains one or more radicals with a variable in the radicand.
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Squaring Property of Equality
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Given real numbers a and b, where a = b, then a2 = b2.
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Extraneous Solution
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A solution that does not solve the original equation.
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Power Property of Equality
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Given any positive integer n and real numbers a and b, where a=b,then an=bn
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Root
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A solution to a quadratic equation in standard form.
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